A transmission system for a vehicle using a combination of a fluid transmission such as a torque converter or fluid coupling, and a stepless transmission which transmits the output torque of the fluid transmission via a V-belt or variable pulley to a vehicle drive shaft after changing the speed in a stepless manner, is disclosed in Tokkai Sho 61-105353 published by the Japanese Patent Office in 1986. A speed change ratio of this stepless transmission is controlled by a controller, and generally varies according to a throttle opening and vehicle speed which represent the acceleration requirement of the driver. Regarding vehicle speed, the higher the vehicle speed, the more the transmission shifts up, i.e., the more the speed change ratio is reduced.
However in some cases, for example when the vehicle start abruptly or when the vehicle starts and accelerates on a road surface which is of a low frictional coefficient, this type of controller may vary the speed change ratio very rapidly when the vehicle skids. As a result, the V-belt or variable pulley may slip, shocks may occur, the driver may experience a feeling of unpleasantness and the controller may suffer wear. This is due to the fact that in general, the vehicle speed is detected from the rotation speed of the drive system, e.g. the drive shaft. In other words, when the drive wheels slip, the speed change controller determines that the vehicle speed has increased, and therefore shifts up. Subsequently, when the drive wheels regain their grip on the road and stop slipping, the controller determines that there has been a sudden drop in vehicle speed. It therefore performs a rapid shift-down and the speed change ratio sharply increases. This causes frictional parts such as belts in the controller to slip, and a shock is produced.